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  • Analytical Derivation of Complex Cell Properties from the Slowness Principle
Analytical Derivation of Complex Cell Properties from the Slowness Principle
Collaborator: Henning Sprekeler

In the project SFA yields complex cell properties we have shown that SFA applied to quasi-natural image sequences yields quadratic functions that share many properties with physiological complex cells in primary visual cortex. Interestingly, the results do not depend on the natural images. If one uses colored noise images, which look like clouds in the sky, one gets the same results. This means that the conditions under which we get complex cell receptive fields can all be formulated analytically: (i) take colored noise images, (ii) generate little movies from them by rotation, translation, and zoom, (iii) rescale all frames of the movies to 16x16 pixels, (iv) apply slow feature analysis (SFA) with quadratic functions, (v) use the resulting quadratic functions as complex cell receptive fields and analyze them - done. As a consequence, one could hope to also solve the problem analytically.

In order to succeed we had to make two simplifying assumptions. Firstly, since dealing with the borders of the receptive fields turned out to be hard, we assumed that the receptive fields are infinitely large and thus have no borders. Secondly, since we have observed in our simulations that translation is the crucial transformation in shaping the receptive fields, we assumed that translation is infinitely faster than rotation or zoom. With these assumption we were able to derive analytical descriptions of the receptive fields, which reproduce a number of important features of those found in simulations and physiological experiments, see figure.

complex cell receptive fields in physiology, simulations, and theory (101 kB)

Figure: A comparison between different complex cell properties in a comparison between physiological experiments, numerical simulations with SFA, and theoretical results.


Publications

    2013

  • Slow Feature Analysis
    Wiskott, L.
    In D. Jaeger & Jung, R. (Eds.), Encyclopedia of Computational Neuroscience Springer-Verlag Berlin Heidelberg
  • 2011

  • Slow feature analysis
    Wiskott, L., Berkes, P., Franzius, M., Sprekeler, H., & Wilbert, N.
    Scholarpedia, 6(4), 5282
  • A theory of Slow Feature Analysis for transformation-based input signals with an application to complex cells
    Sprekeler, H., & Wiskott, L.
    Neural Computation, 23(2), 303–335
  • 2009

  • Slowness learning
    Sprekeler, H.
    Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I
  • 2007

  • Is slowness a learning principle of the visual system?
    Wiskott, L., Franzius, M., Berkes, P., & Sprekeler, H.
    In A. Treves, Battaglini, P. P., Chelazzi, L., Diamond, M., & Vallortigara, G. (Eds.), Proc. 39th European Brain and Behaviour Society Meeting (EBBS), Sep 15–19, Triest, Italy (pp. 14–15)
  • Towards an analytical derivation of complex cell receptive field properties
    Wiskott, L., Sprekeler, H., & Berkes, P.
    In Proc. 7th Göttingen Meeting of the German Neuroscience Society, Mar 29 – Apr 1, Göttingen, Germany (pp. S12–2)
  • 2006

  • Analytical derivation of complex cell properties from the slowness principle
    Sprekeler, H., & Wiskott, L.
    In Proc. 2nd Bernstein Symposium for Computational Neuroscience, Oct 1–3, Berlin, Germany (p. 67) Bernstein Center for Computational Neuroscience (BCCN) Berlin
  • Analytical derivation of complex cell properties from the slowness principle
    Sprekeler, H., & Wiskott, L.
    In Proc. Conference on Mathematical Neuroscience (NEUROMATH 06), Sep 1-4, Andorra (p. 62)
  • Analytical derivation of complex cell properties from the slowness principle
    Sprekeler, H., & Wiskott, L.
    In Proc. Berlin Neuroscience Forum, Jun 8–10, Bad Liebenwalde, Germany (pp. 65–66) Berlin: Max-Delbrück-Centrum für Molekulare Medizin (MDC)
  • Analytical derivation of complex cell properties from the slowness principle
    Sprekeler, H., & Wiskott, L.
    In Proc. 15th Annual Computational Neuroscience Meeting (CNS′06), Jul 16–20, Edinburgh, Scotland

The Institut für Neuroinformatik (INI) is a central research unit of the Ruhr-Universität Bochum. We aim to understand the fundamental principles through which organisms generate behavior and cognition while linked to their environments through sensory systems and while acting in those environments through effector systems. Inspired by our insights into such natural cognitive systems, we seek new solutions to problems of information processing in artificial cognitive systems. We draw from a variety of disciplines that include experimental approaches from psychology and neurophysiology as well as theoretical approaches from physics, mathematics, electrical engineering and applied computer science, in particular machine learning, artificial intelligence, and computer vision.

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